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\section{Abstract}
\section{Introduction}
\subsection{Fisher}
\subsection{Chemical Kinetics and Disorder}
\section{Pre-Theory Background}
\subsection{GFE}
\subsection{Fisher Information}
\subsection{inequality}
\section{Absolute Formulation}
\subsection{Rate}
\subsection{Fisher Information}
\subsection{GFE to FE}
\subsection{Inequality}
\section{Relative Formulation}
\subsection{Rate}
\subsection{Fisher Information}
\subsection{GFE to FE}
\subsection{Inequality}
\section{All S Formulation}
\subsection{Rate}
\subsection{Fisher Information}
\subsection{GFE to FE}
\subsection{Inequality}
\section{Connections Bewteen Relative Absolute and All S}
\section{Connections to First Paper}
\section{The difference in the I(t) Formulations}
In the first paper we did not use the formal definition of the Fisher Information proposed by R J Fisher, we instead changed the way in which we scaled the function. However we can explicitly show that our specific formulation is consistent with the definition proposed by Fisher when you consider a specific assumption we made, namely a single survival function describing the trajectories of the system. For convenience we will label our formulation of the Fisher Information as $I_1$ the traditional definition of the Fisher Information as $I_2$.
\begin{equation}
I_1\equiv I(t)=\sum S_i(t)(\frac{d}{dt}[ln\sum S_i(t)])^2
\end{equation}
\begin{equation}
I_2\equiv \frac{I_i(t)}{\sum S_i(t)}=\frac{S_i(t)}{\sum S_i(t)}(\frac{d}{dt}[lnS(t)])^2=\sum \gamma_i(\frac{d}{dt}[lnS(t)])^2
\end{equation}
Now what if we look at the example from the first paper where there is only one $S_i(t)\equiv S(t)$, this example shows that these two formulations collapse into the same result.
\begin{equation}
I_1=S(t)(\frac{d}{dt}[lnS(t)])^2
\end{equation}
If we now divide both sides by S(t) we find the following
\begin{equation}
\frac{I_1}{S(t)}=(\frac{d}{dt}[lnS(t)])^2
\end{equation}
Lets now look at this simplified form of $I_2$.
\begin{equation}
I_2=\frac{S(t)}{S(t)}(\frac{d}{dt}[lnS(t)])^2=(\frac{d}{dt}[lnS(t)])^2
\end{equation}
Therefore the formulation within the first paper is a result of the single survival function approximation, and it is consistent with our now generalized approach.
\section{Applications, a complete analysis of two seperate A states}
\section{ Conclusion}
To synthesize this work we construct a simple cycle connecting the GFE and the FE that applies to all three formulations of the rates, Fisher Information, and the GFE's.
\section{Rates, three $I(t)$, three GFEs}
\subsection{Rates}